2 The resonant switch concept A quite general idea: 1. PWM switch network is replaced by a resonant switch network. This leads to a quasi-resonant version of the original PWM converter Example: realization of the switch cell in the buck converter i L i PWM switch cell i v g v 1 Switch cell C R v v 1 Fundamentals of Power Electronics Chapter 0: Quasi-Resonant Converters

5 Averaged switch modeling of ZCS cells It is assumed that the converter filter elements are large, such that their switching ripples are small. Hence, we can make the small ripple approximation as usual, for these elements: i i Ts v 1 v 1 Ts In steady state, we can further approximate these quantities by their dc values: i I v 1 V 1 Modeling objective: find the average values of the terminal waveforms T s and T s Fundamentals of Power Electronics 5 Chapter 0: Quasi-Resonant Converters

11 Boundary of zero current switching If the requirement I < V 1 R 0 is violated, then the inductor current never reaches zero. In consequence, the transistor cannot switch off at zero current. The resonant switch operates with zero current switching only for load currents less than the above value. The characteristic impedance must be sufficiently small, so that the ringing component of the current is greater than the dc load current. Capacitor voltage at the end of subinterval is (α β)=v c1 = V I R 0 V 1 Fundamentals of Power Electronics 11 Chapter 0: Quasi-Resonant Converters

13 Subinterval 4 Subinterval 4, of angular length ξ, is identical to the diode conduction interval of the conventional PWM switch network. Diode conducts the filter inductor current I The tank capacitor voltage is equal to zero. Transistor Q 1 is off, and the input current is equal to zero. The length of subinterval 4 can be used as a control variable. Increasing the length of this interval reduces the average output voltage. Fundamentals of Power Electronics 13 Chapter 0: Quasi-Resonant Converters

14 Maximum switching frequency The length of the fourth subinterval cannot be negative, and the switching period must be at least long enough for the tank current and voltage to return to zero by the end of the switching period. The angular length of the switching period is ω 0 T s = α β δ ξ = π f 0 = f π s F where the normalized switching frequency F is defined as F = f s f 0 So the minimum switching period is ω 0 T s α β δ Substitute previous solutions for subinterval lengths: π I R 0 π sin F V 1 I R 0 V I R 0 1 V 1 I R 0 V 1 Fundamentals of Power Electronics 14 Chapter 0: Quasi-Resonant Converters

28 A test to determine the topology of a resonant switch network Replace converter elements by their high-frequency equivalents: Independent voltage source V g : short circuit Filter capacitors: short circuits Filter inductors: open circuits The resonant switch network remains. If the converter contains a ZCS quasi-resonant switch, then the result of these operations is SW Fundamentals of Power Electronics 8 Chapter 0: Quasi-Resonant Converters

44 0.4 Summary of key points 1. In a resonant switch converter, the switch network of a PWM converter is replaced by a switch network containing resonant elements. The resulting hybrid converter combines the properties of the resonant switch network and the parent PWM converter.. Analysis of a resonant switch cell involves determination of the switch conversion ratio µ. The resonant switch waveforms are determined, and are then averaged. The switch conversion ratio µ is a generalization of the PWM CCM duty cycle d. The results of the averaged analysis of PWM converters operating in CCM can be directly adapted to the related resonant switch converter, simply by replacing d with µ. 3. In the zero-current-switching quasi-resonant switch, diode operates with zero-voltage switching, while transistor Q 1 and diode D 1 operate with zero-current switching. Fundamentals of Power Electronics 44 Chapter 0: Quasi-Resonant Converters

45 Summary of key points 4. In the zero-voltage-switching quasi-resonant switch, the transistor Q 1 and diode D 1 operate with zero-voltage switching, while diode operates with zero-current switching. 5. Full-wave versions of the quasi-resonant switches exhibit very simple control characteristics: the conversion ratio µ is essentially independent of load current. However, these converters exhibit reduced efficiency at light load, due to the large circulating currents. In addition, significant switching loss is incurred due to the recovered charge of diode D Half-wave versions of the quasi-resonant switch exhibit conversion ratios that are strongly dependent on the load current. These converters typically operate with wide variations of switching frequency. 7. In the zero-voltage-switching multiresonant switch, all semiconductor devices operate with zero-voltage switching. In consequence, very low switching loss is observed. Fundamentals of Power Electronics 45 Chapter 0: Quasi-Resonant Converters

46 Summary of key points 8. In the quasi-square-wave zero-voltage-switching resonant switches, all semiconductor devices operate with zero-voltage switching, and with peak voltages equal to those of the parent PWM converter. The switch conversion ratio is restricted to the range 0.5 µ The small-signal ac models of converters containing resonant switches are similar to the small-signal models of their parent PWM converters. The averaged switch modeling approach can be employed to show that the quantity d is simply replaced by µ. 10.In the case of full-wave quasi-resonant switches, µ depends only on the switching frequency, and therefore the transfer function poles and zeroes are identical to those of the parent PWM converter. 11.In the case of half-wave quasi-resonant switches, as well as other types of resonant switches, the conversion ratio µ is a strong function of the switch terminal quantities v 1 and i. This leads to effective feedback, which modifies the poles, zeroes, and gains of the transfer functions. Fundamentals of Power Electronics 46 Chapter 0: Quasi-Resonant Converters

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